A covering system of this kind is already known from DE 10 2010 047 242 A1. In the known system, heat insulation panels may be affixed to a construction-side subsurface, such as masonry, by anchoring elements in the manner of plug screws. Retaining plates that protrude slightly from the outside of the heat insulation panels are located at the ends of the anchoring elements facing away from the construction-side subsurface. The retaining plates form mounting locations for components, for example in the form of plate-shaped facade elements. These structural elements are anchored by a touch-and-close fastening, formed out of touch-and-close fastening elements. These elements are fixed on the side of the heat insulation panels to the plate-shaped mounting locations and are fixed by touch-and-close fastening elements of a connecting device that correspond thereto. The elements are located on the side of the plate-shaped component that is facing the heat insulation panels. This connecting device has a support surface, which, having one side in contact with a large area of the respective plate-shaped component, is permanently connected thereto, and which, at the other side of said support surface, forms the touch-and-close fastening elements, which can be engaged in an adhesive-like engagement with the corresponding touch-and-close fastening elements at the plate-like mounting locations. This type of anchoring by forming a touch-and-close fastening permits quick and easy affixing of the plate-shaped structural elements. An advantageous option is subsequently adjusting or, if necessary, exchanging structural elements by releasing the touch-and-close fastening. The known solution is not satisfactory in so far as the dependability of the fixture is dependent on the condition of the plate-shaped structural elements. As a result, the reliable attachment of the support surface having the touch-and-close fastening elements is thus strongly dependent on the surface condition of the respective component that is to be affixed. One is then limited to the use of materials that are suitable for the facade element that is to be affixed. In particular, difficulties arise in the case of structural elements made out of closed-celled foam materials.